7 papers
Boundary-compatible interacting approximations of quasilinear PDEs on bounded domains
Thierry Paul, Emmanuel Trélat
We develop a general operator-theoretic route that turns Kato-type quasilinear evolution systems on a Banach scale into finite-dimensional interacting approximations. The c…
Multi-agent systems with multiple-wise interaction: Propagation of chaos and macroscopic limit
Thierry Paul, Stefano Rossi, Emmanuel Trélat
We consider interacting multi-agent systems where the interaction is not only pairwise but involves simultaneous interactions among multiple agents (multiple-wise interaction). By…
Numerical modeling of flocking dynamics with topological interactions
Marta Menci, Thierry Paul, Stefano Rossi +1
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macro…
Universal approximations of quasilinear PDEs by finite distinguishable particle systems
Thierry Paul, Emmanuel Trélat
In this paper, we prove that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N distinguishable particles, to within 1/ ln(N ).…
From microscopic to macroscopic: the large number dynamics of agents and cells, possibly interacting with a chemical background
Thierry Paul
In this paper we review some recent results dealing with the transition between microscopic and macroscopic scales in different fields, including kinetic theory, cells movement in…
The Random Batch Method for -Body Quantum Dynamics
François Golse, Shi Jin, Thierry Paul
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total in…
From Toda to KdV
Dario Bambusi, Thomas Kappeler, Thierry Paul
For periodic Toda chains with a large number of particles we consider states which are -close to the equilibrium and constructed by discretizing arbitrary given f…